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Conjugate natural heat transfer scrutiny in differentially heated cavity partitioned with a conducting solid using the lattice Boltzmann method

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Abstract

In the present paper, we numerically investigated the two-dimensional conjugate heat transfer problems in a unitary computational domain containing both the solid and fluid regions. The physical problem configuration consists of two adiabatic horizontal walls of finite thickness and two vertical walls; the left one is maintained at hot temperature Th and the right one is maintained at cold temperature Tc. The lattice Boltzmann method (LBM) based on the BGK model has been used to simulate laminar natural convection in the partitioned air-filled cavity with a heat-conducting solid. In the interface boundaries of the heat-conducting solid, the continuity of temperature and heat transfer is considered. A series of numerical simulation is carried out over a wide range of the Rayleigh number (Ra = 103–106), the thermal conductivity ratio kr and the solid partition thickness (δ = 1–95℅) and its horizontal position. The results show that the partition reduces the heat transfer rate in the cavity. For a centered partition (Xs = 0.5), the average Nusselt number decreases almost linearly with partition thickness for δ ≤ 0.45; however, it increases for δ ≥ 0.45 due to the confinement in the thin fluid regions. For Ra = 105, the heat transfer rate decreases with the partition position until a critical value close to 0.325 and rises slightly until Xs = 0.5. The critical position value decreases with the Ra number increase and it is close to 0.2 for Ra = 106 where Nu = 3.766. The heat transfer rate is enhanced with the increase in thermal conductivity. Correlations of the average Nusselt numbers are obtained as a function of Rayleigh number.

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Abbreviations

c :

Lattice speed

c s :

Lattice speed of sound

c i :

Discrete particle speed

f :

Density distribution functions

f eq :

ρ-equilibrium distribution functions

g :

Temperature distribution functions

g eq :

θ-equilibrium distribution functions

ω i :

Weight factor

k f :

Fluid thermal conductivity (W m−1 K−1)

k s :

Solid thermal conductivity (W m−1 K−1)

k r :

Thermal conductivity ratio

m, n :

Lattice cell numbers

Nu :

Local Nusselt number = ∂θ/∂X

\(\overline{Nu}\) :

Average Nusselt number =  \(\int_{Y = 0}^{1} {Nu\,{\text{d}}Y}\)

p :

Pressure (Pa)

Ra :

Rayleigh number = Ra = gβ(Th − Tc)W3/αυ

Pr :

Prandtl number = υ/α

T :

Temperature (K)

T c :

Temperature of the cold wall (K)

T h :

Temperature of the hot wall (K)

u, v :

Dimensional velocities (m s−1)

U, V :

Non-dimensional velocities

H :

Height of the cavity (m)

W :

Width of the cavity (m)

x, y :

Coordinates system (–)

X, Y :

Non-dimensional Cartesian coordinates

X s :

Position of the partition

t :

Time (s)

α :

Thermal diffusivity (m2 s−1)

β :

Coefficient of thermal expansion (K−1)

Δx :

Lattice spacing

Δt :

Time increment (s)

μ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Fluid density (kg m−3)

τ α :

Relaxation time for temperature (m2 s−1)

τ υ :

Relaxation time for flow (m2 s−1)

θ :

Non-dimensional temperature

υ :

Kinematic viscosity (m2 s−1)

δ :

Thickness of the conducting body (m)

τ :

Dimensionless time

c:

Cold surface

f:

Fluid

h:

Hot surface

s:

Solid

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Authors and Affiliations

  1. Higher National Engineering School of Tunis, University of Tunis, 5 Avenue Taha Hussein, 1008, Tunis, Tunisia

    M. Ferhi

  2. LR: Subatomic Physics, Nanoscience and Energetics, IPEST, La Marsa, University of Carthage, Tunis, 2070, Tunisia

    M. Ferhi & R. Djebali

  3. ICB, UMR 6303, CNRS, Université de Bourgogne Franche-Comté, UTBM Département COMM, 90010, Belfort, France

    S. Abboudi

  4. UR: Renewable Energy for Agriculture and Agro-Industry, ESIM, University of Jendouba, Jendouba, Tunisia

    H. Kharroubi

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Ferhi, M., Djebali, R., Abboudi, S. et al. Conjugate natural heat transfer scrutiny in differentially heated cavity partitioned with a conducting solid using the lattice Boltzmann method. J Therm Anal Calorim 138, 3065–3088 (2019). https://doi.org/10.1007/s10973-019-08276-8

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